At least 1 hour before serving, place 2 martini glasses in the freezer.
Fill a cocktail shaker with ice. Pour the rye, Campari and vermouth in the cocktail shaker. Gently stir a few times, pausing between stirs as you want the ice to cool and dilute the mixture. With a cocktail strainer, pour the drink into the chilled martini glasses. Garnish with the orange peel twists. Serve ice cold.